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ehrenfest
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[SOLVED] rings with unity
Corollary 27.18 (in Farleigh) tells us that every ring with unity contains a subring isomorphic to either Z or some Z_n. Is it possible that a ring with unity may simultaneously contain two subrings isomorphic to Z_n and Z_n with n not equal to m? If it is possible, give an example. If it is impossible, prove it.
EDIT: change the second Z_n to Z_m
My intuition tells me it is impossible. But I have no idea how to prove it.
Homework Statement
Corollary 27.18 (in Farleigh) tells us that every ring with unity contains a subring isomorphic to either Z or some Z_n. Is it possible that a ring with unity may simultaneously contain two subrings isomorphic to Z_n and Z_n with n not equal to m? If it is possible, give an example. If it is impossible, prove it.
EDIT: change the second Z_n to Z_m
Homework Equations
The Attempt at a Solution
My intuition tells me it is impossible. But I have no idea how to prove it.
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